Question: Express this quotient in scientific notation: ${\frac{4.800\times 10^{-4}} {5.0\times 10^{-5}}}$
Answer: Start by collecting like terms together. $= {\frac{4.800} {5.0}} \times{\frac{10^{-4}} {10^{-5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.96 \times 10^{-4\,-\,-5}$ $= 0.96 \times 10^{1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.96$ is the same as $9.60 \div 10$ , or $9.60 \times 10^{-1}$ $ = {9.60 \times 10^{-1}} \times 10^{1} $ $= 9.60\times 10^{0}$